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7-1

7-1

Exploring Exponential Models

exponential function

exponential growth

exponential decay

growth factor

decay factor

1. Is an exponential model reasonable for this situation? Explain.

1. In the function y 5 12(2.3)x , the value 2.3 is the growth factor . asymptote 2. An

Yes; the population decreases at a ﬁxed, constant rate of 3.5% per year.

is a line that a graph approaches as x or y increases in

An exponential model is reasonable

absolute value. exponential decay

3. For

Exploring Exponential Models

Population The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 of the animals in the habitat you are studying.

a. Write a function that models the change in the animal population.

b. Graphing Calculator Graph the function. Estimate the number of years until the population first drops below 15 animals.

Choose the word or phrase from the list that best completes each sentence.

asymptote

Think About a Plan

.

a(1 1 r) z

2. Write the function that models exponential growth or decay. A(t) 5 z t , as the value of x increases, the value of y

decreases.

4. A function in the general form y 5 abx is called an exponential function .

animals z .

3. The initial population is z 80

5. For exponential growth , as the value of x increases, the value of y

4. Is the rate of change positive or negative? Explain.

increases.

The population is decreasing, so the rate of change is negative

6. In the function y 5 4(0.3)x , the value 0.3 is the

decay factor

.

z

.

z

5. The rate of change is 20.035 .

Identify whether each function represents exponential growth or exponential decay. 7. y 5 0.75(4)x

exponential growth

8. y 5 0.63(0.5)x

exponential decay

9. y 5 9(0.83)x

exponential decay

t

6. Write a function that models the change in the animal population. P(t) 5 z 80(0.965) z

7. Graph your function on a graphing calculator. Sketch